Relative Velocity when Two Velocities Inclined to Each Other

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The figure above shows two cars moving with velocities inclined to each other at an angle q. Let the relative velocity of with respect to .

However, from the parallelogram of vectors OABC,

In a similar way, the relative velocity V_A with respect to V_B, that is, V_AB can also be determined. The figure below illustrates this case. It can be seen that the magnitude of relative velocity in both cases is the same with the direction reversed.

Special cases

1) When both the cars are moving in the same direction, i.e., q = 0⁰ degrees.

Thus, the relative speed between two bodies moving in the same direction is equal to the difference of the individual speeds of two bodies.

2) When the two cars are moving along parallel lines in opposite direction, i.e., q = 180⁰ degrees.

Then

However, relative speeds cannot be negative.

i.e., the relative speed between two bodies moving in opposite directions is equal to the sum of the individual speeds.

Rain and man

This is an example in which a man can hold his umbrella properly by making use of the concept of relative velocity.

The figure above shows a man walking due east with a velocity . The rain is falling vertically with a velocity . The relative velocity of rain w.r.t the man is calculated in the following way.

Applying the law of triangle of velocities.

Moreover, tan q = V_m / V_r which gives the angle at which the man can hold his umbrella with the vertical, in order to protect himself from the rain.